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Answer:
Let first term= a common difference = d
16th term = a + 15d
3rd term = a+ 2d
Given
a+ 15 d = 5( a + 2d)
a + 15d = 5a + 10d
5 d = 4a
so [a = 5/4 d ]
Now 10th term = a + 9d = 41
Putting value of a in this
5/4 d + 9d = 41
[ 5d + 36d ] = 41 * 4
41 d = 41 *4
d = [41* 4] / 41
d = 4
a = 5/4 * 4
a= 5
Sum of first 15 terms = 15/2 [ 2a + 14d]
= 15/2 [ 10 + 56 ]
= 15/2 [ 66]
= 15 [ 33]
= 495
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